CN111291315A - Data processing method, device and equipment - Google Patents

Data processing method, device and equipment Download PDF

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CN111291315A
CN111291315A CN201811488764.4A CN201811488764A CN111291315A CN 111291315 A CN111291315 A CN 111291315A CN 201811488764 A CN201811488764 A CN 201811488764A CN 111291315 A CN111291315 A CN 111291315A
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金晓成
余作奔
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China Academy of Telecommunications Technology CATT
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Abstract

The invention provides a data processing method, a device and equipment, wherein the data processing method comprises the following steps: carrying out Fourier transform on preset discrete signal data to obtain Fourier series; splitting the Fourier series to obtain a twiddle factor; wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave. According to the scheme, Fourier transform is carried out on preset discrete signal data to obtain Fourier series; splitting the Fourier series to obtain a twiddle factor; wherein, the rotation factor includes non-integer frequency shift amount of carrier wave; the FFT operation can be completed under the condition of not increasing the calculated amount, the data processing amount is reduced, and the problem of large processing amount of the data processing scheme in the prior art is well solved; and the processing mode of the scheme is suitable for all non-integer frequency shifted carrier frequencies and all butterfly operations (including FFT operations of various bases and mixed bases), and has better compatibility with the traditional FFT operation.

Description

Data processing method, device and equipment
Technical Field
The present invention relates to the field of data processing technologies, and in particular, to a data processing method, apparatus, and device.
Background
Fast Fourier Transform (FFT) greatly reduces the computational complexity of DFT based on butterfly operation, so that DFT is widely applied in actual scenes. In an actual application scenario, the mathematical expression of a part of signals is not completely consistent with the mathematical expression of DFT, for example, carrier frequencies have non-integer frequency shifts, so that certain processing needs to be performed before FFT operation, and accordingly, an extra calculation amount needs to be added.
Wherein, 1) with respect to FFT algorithm background:
the periodic discrete fourier transform pair can be represented as:
Figure BDA0001895173290000011
Figure BDA0001895173290000012
wherein, x [ n ]]For discrete-time signals, N is x [ N ]]Minimum positive period of (a)kIs a Fourier series, omega02 pi/N is the fundamental frequency.
In a practical application scenario, it may be referred to a case that the carrier frequency contains a non-integer frequency shift. For example, in Long Term Evolution (LTE), the time continuous signal s (t) in the uplink timeslot can be expressed as:
Figure BDA0001895173290000013
wherein ,
Figure BDA0001895173290000014
as the number of the effective sub-carriers,
Figure BDA0001895173290000015
(indicating rounding down), Δ f 15kHz is the subcarrier spacing, NCPIs a cyclic prefix, T, of an Orthogonal Frequency Division Multiplexing (OFDM) symbol s1/(15000 × 2048) s is a basic time unit of LTE.
Discretizing and simplifying equation (3) can easily obtain the following expression:
Figure BDA0001895173290000021
wherein ,
Figure BDA0001895173290000022
since the carrier frequencies of equation (1) and equation (4) are different, two different symbols are used to represent the discrete-time signal.
The corresponding DFT operation can be expressed as:
Figure BDA0001895173290000023
wherein, S [ k ]]＝ak。
Comparing equation (2) and equation (5) shows that they differ by a sub-carrier frequency shift of 1/2. If the FFT operation is performed, the 1/2 carrier frequency shift needs to be processed in advance, so that the extra calculation amount is inevitably required.
2) Regarding the conventional DFT processing method:
the equation (5) is equivalently transformed to obtain:
Figure BDA0001895173290000024
wherein ,
Figure BDA0001895173290000025
equation (6) is equivalent to the preceding pair of data sequences s' [ n ]]Performing phase rotation to change the phase into x [ n ]]Therefore, FFT operation can be applied.
That is, as shown in equation (6), the conventional method for processing the carrier non-integer frequency shift requires phase rotation of the data sequence in advance, and then conventional FFT operation. It is known that the FFT operation is to reduce the number of times of multiplication and addition of DFT in a computer. Under the carrier non-integer frequency shift, the conventional method needs to add N times of complex multiplication operations. The conventional method thus increases the computational burden of the computer to some extent.
Therefore, the conventional scheme for performing data processing in the above manner has a problem of large processing amount.
Disclosure of Invention
The invention aims to provide a data processing method, a data processing device and data processing equipment, and solves the problem that a data processing scheme in the prior art is large in processing capacity.
In order to solve the above technical problem, an embodiment of the present invention provides a data processing method, including:
carrying out Fourier transform on preset discrete signal data to obtain Fourier series;
splitting the Fourier series to obtain a twiddle factor;
wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave.
Optionally, the splitting the fourier series to obtain the twiddle factor includes:
splitting the Fourier series by using a formula I to obtain a partial number of twiddle factors;
the first formula is as follows:
Figure BDA0001895173290000031
wherein ,akRepresenting a Fourier series, S[l][k]Is shown askPerforming butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data, e representing a natural constant, N representing an nth accumulation term, N being greater than or equal to 0 and less than or equal to N-1, k representing an integer frequency shift amount of the carrier, k being greater than or equal to 0 and less than or equal to N/l-1, α representing a non-integer frequency shift amount of the carrier, s [ N ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000032
Figure BDA0001895173290000033
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000034
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000035
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000036
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000037
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA0001895173290000038
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure BDA0001895173290000039
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900000310
Figure BDA00018951732900000311
alternatively to this, the first and second parts may,
Figure BDA00018951732900000312
the method specifically comprises the following steps:
Figure BDA0001895173290000041
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000042
Figure BDA0001895173290000043
optionally, the splitting the fourier series to obtain the twiddle factor further includes:
splitting the Fourier series by using a formula II to obtain twiddle factors of the rest number;
the second formula is:
Figure BDA0001895173290000044
wherein ,
Figure BDA0001895173290000045
the number of fourier series is represented,
Figure BDA0001895173290000046
show that
Figure BDA0001895173290000047
Performing butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; i represents i
Figure BDA0001895173290000051
I is more than or equal to 0 and less than or equal to l-1, α represents non-integer frequency shift quantity of carrier wave, s [ n ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000052
Figure BDA0001895173290000053
to representThe 0 th accumulated entry for the base l,
Figure BDA0001895173290000054
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000055
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000056
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000057
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA0001895173290000058
representing the twiddle factor corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000059
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900000510
alternatively to this, the first and second parts may,
Figure BDA00018951732900000511
the method specifically comprises the following steps:
Figure BDA0001895173290000061
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000062
representing the intermediate operational coefficient corresponding to the 1 st accumulation term,
Figure BDA0001895173290000063
representing the intermediate operational coefficients corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000064
represents an intermediate operation coefficient corresponding to the l-1 st accumulation term, and
Figure BDA0001895173290000065
Figure BDA0001895173290000071
Figure BDA0001895173290000072
an embodiment of the present invention further provides a data processing device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor; the processor implements the following steps when executing the program:
carrying out Fourier transform on preset discrete signal data to obtain Fourier series;
splitting the Fourier series to obtain a twiddle factor;
wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave.
Optionally, the processor is specifically configured to:
splitting the Fourier series by using a formula I to obtain a partial number of twiddle factors;
the first formula is as follows:
Figure BDA0001895173290000073
wherein ,akRepresenting a Fourier series, S[l][k]Is shown askPerforming butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data, e representing a natural constant, N representing an nth accumulation term, N being greater than or equal to 0 and less than or equal to N-1, k representing an integer frequency shift amount of the carrier, k being greater than or equal to 0 and less than or equal to N/l-1, α representing a non-integer frequency shift amount of the carrier, s [ N ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000074
Figure BDA0001895173290000075
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000076
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000077
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000078
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000079
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA00018951732900000710
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure BDA00018951732900000711
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900000712
Figure BDA00018951732900000713
alternatively to this, the first and second parts may,
Figure BDA00018951732900000714
the method specifically comprises the following steps:
Figure BDA0001895173290000081
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000082
Figure BDA0001895173290000083
optionally, the processor is further configured to:
splitting the Fourier series by using a formula II to obtain twiddle factors of the rest number;
the second formula is:
Figure BDA0001895173290000084
wherein ,
Figure BDA0001895173290000085
the number of fourier series is represented,
Figure BDA0001895173290000086
show that
Figure BDA0001895173290000087
Performing butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]To representThe preset discrete signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; i represents i
Figure BDA0001895173290000091
I is more than or equal to 0 and less than or equal to l-1, α represents non-integer frequency shift quantity of carrier wave, s [ n ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000092
Figure BDA0001895173290000093
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000094
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000095
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000096
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000097
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA0001895173290000098
representing the twiddle factor corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000099
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900000910
alternatively to this, the first and second parts may,
Figure BDA00018951732900000911
the method specifically comprises the following steps:
Figure BDA0001895173290000101
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000102
representing the intermediate operational coefficient corresponding to the 1 st accumulation term,
Figure BDA0001895173290000103
representing the intermediate operational coefficients corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000104
represents an intermediate operation coefficient corresponding to the l-1 st accumulation term, and
Figure BDA0001895173290000105
Figure BDA0001895173290000111
Figure BDA0001895173290000112
an embodiment of the present invention further provides a data processing apparatus, including:
the first processing module is used for carrying out Fourier transform on preset discrete signal data to obtain Fourier series;
the first splitting module is used for splitting the Fourier series to obtain a twiddle factor;
wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave.
Optionally, the first splitting module includes:
the first splitting submodule is used for splitting the Fourier series by using a formula I to obtain a partial number of twiddle factors;
the first formula is as follows:
Figure BDA0001895173290000113
wherein ,akRepresenting a Fourier series, S[l][k]Is shown askPerforming butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data, e representing a natural constant, N representing an nth accumulation term, N being greater than or equal to 0 and less than or equal to N-1, k representing an integer frequency shift amount of the carrier, k being greater than or equal to 0 and less than or equal to N/l-1, α representing a non-integer frequency shift amount of the carrier, s [ N ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000114
Figure BDA0001895173290000115
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000116
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000117
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000118
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000119
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA00018951732900001110
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure BDA00018951732900001111
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900001112
Figure BDA00018951732900001113
alternatively to this, the first and second parts may,
Figure BDA00018951732900001114
the method specifically comprises the following steps:
Figure BDA0001895173290000121
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000122
Figure BDA0001895173290000123
optionally, the first splitting module further includes:
the second splitting submodule is used for splitting the Fourier series by using a formula II to obtain the twiddle factors of the rest number;
the second formula is:
Figure BDA0001895173290000124
wherein ,
Figure BDA0001895173290000131
the number of fourier series is represented,
Figure BDA0001895173290000132
show that
Figure BDA0001895173290000133
Performing butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; i represents i
Figure BDA0001895173290000134
I is more than or equal to 0 and less than or equal to l-1, α represents non-integer frequency shift quantity of carrier wave, s [ n ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000135
Figure BDA0001895173290000136
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000137
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000138
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000139
the l-1 st cumulative term representing the base l;
Figure BDA00018951732900001310
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA00018951732900001311
representing the twiddle factor corresponding to the 2 nd accumulation term,
Figure BDA00018951732900001312
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900001313
alternatively to this, the first and second parts may,
Figure BDA00018951732900001314
the method specifically comprises the following steps:
Figure BDA0001895173290000141
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000142
representing the intermediate operational coefficient corresponding to the 1 st accumulation term,
Figure BDA0001895173290000143
representing the intermediate operational coefficients corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000144
represents an intermediate operation coefficient corresponding to the l-1 st accumulation term, and
Figure BDA0001895173290000145
Figure BDA0001895173290000151
Figure BDA0001895173290000152
embodiments of the present invention also provide a computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the data processing method described above.
The technical scheme of the invention has the following beneficial effects:
in the scheme, the data processing method performs Fourier transform on preset discrete signal data to obtain Fourier series; splitting the Fourier series to obtain a twiddle factor; wherein, the rotation factor includes non-integer frequency shift amount of carrier wave; the method can realize that the FFT operation is completed under the condition of not increasing the calculation amount, and the data processing amount is reduced, and can be embodied in the following steps: in the uplink time slot of LTE, as the operation times are reduced and the data processing amount is reduced compared with the prior scheme, the processing time delay can be effectively reduced, the processing memory can be saved and the implementation complexity can be reduced; the problem of large processing capacity of a data processing scheme in the prior art is well solved; and the processing mode of the scheme is suitable for all non-integer frequency shifted carrier frequencies and all butterfly operations (including FFT operations of various bases and mixed bases), and has better compatibility with the traditional FFT operation.
Drawings
FIG. 1 is a flow chart of a data processing method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a radix-2 butterfly operation process according to an embodiment of the invention;
FIG. 3 is a flow chart illustrating a radix-3 butterfly operation according to an embodiment of the invention;
FIG. 4 is a schematic flow chart illustrating a 6-point DFT implemented by mixed-radix butterfly operation according to an embodiment of the present invention;
FIG. 5 is a block diagram of a data processing apparatus according to an embodiment of the present invention;
FIG. 6 is a block diagram of a data processing apparatus according to an embodiment of the present invention;
fig. 7 is a schematic diagram of an implementation of fast fourier transform according to an embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
The present invention provides a data processing method, as shown in fig. 1, for solving the problem of large processing capacity of the data processing scheme in the prior art, including:
step 11: carrying out Fourier transform on preset discrete signal data to obtain Fourier series;
step 12: splitting the Fourier series to obtain a twiddle factor;
wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave.
According to the data processing method provided by the embodiment of the invention, Fourier transform is carried out on preset discrete signal data to obtain Fourier series; splitting the Fourier series to obtain a twiddle factor; wherein, the rotation factor includes non-integer frequency shift amount of carrier wave; the method can realize that the FFT operation is completed under the condition of not increasing the calculation amount, and the data processing amount is reduced, and can be embodied in the following steps: in the uplink time slot of LTE, as the operation times are reduced and the data processing amount is reduced compared with the prior scheme, the processing time delay can be effectively reduced, the processing memory can be saved and the implementation complexity can be reduced; the problem of large processing capacity of a data processing scheme in the prior art is well solved; and the processing mode of the scheme is suitable for all non-integer frequency shifted carrier frequencies and all butterfly operations (including FFT operations of various bases and mixed bases), and has better compatibility with the traditional FFT operation.
Splitting the Fourier series to obtain a twiddle factor, wherein the splitting of the Fourier series comprises the following steps:
splitting the Fourier series by using a formula I to obtain a partial number of twiddle factors;
the first formula is as follows:
Figure BDA0001895173290000161
wherein ,akRepresenting a Fourier series, S[l][k]Is shown askPerforming butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data, e representing a natural constant, N representing an nth accumulation term, N being greater than or equal to 0 and less than or equal to N-1, k representing an integer frequency shift amount of the carrier, k being greater than or equal to 0 and less than or equal to N/l-1, α representing a non-integer frequency shift amount of the carrier, s [ N ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000162
Figure BDA0001895173290000163
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000164
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000165
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000166
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000167
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA0001895173290000168
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure BDA0001895173290000171
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA0001895173290000172
Figure BDA0001895173290000173
in particular, the method comprises the following steps of,
Figure BDA0001895173290000174
the method specifically comprises the following steps:
Figure BDA0001895173290000175
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000176
Figure BDA0001895173290000177
further, the splitting the fourier series to obtain the twiddle factor further includes:
splitting the Fourier series by using a formula II to obtain twiddle factors of the rest number;
the second formula is:
Figure BDA0001895173290000181
wherein ,
Figure BDA0001895173290000182
the number of fourier series is represented,
Figure BDA0001895173290000183
show that
Figure BDA0001895173290000184
Performing butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; i represents i
Figure BDA0001895173290000185
I is more than or equal to 0 and less than or equal to l-1, α represents non-integer frequency shift quantity of carrier wave, s [ n ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000186
Figure BDA0001895173290000187
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000188
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000189
the 2 nd accumulated term representing the base l,
Figure BDA00018951732900001810
the l-1 st cumulative term representing the base l;
Figure BDA00018951732900001811
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA00018951732900001812
representing the twiddle factor corresponding to the 2 nd accumulation term,
Figure BDA00018951732900001813
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900001814
in particular, the method comprises the following steps of,
Figure BDA00018951732900001815
the method specifically comprises the following steps:
Figure BDA0001895173290000191
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000192
representing the intermediate operational coefficient corresponding to the 1 st accumulation term,
Figure BDA0001895173290000193
representing the intermediate operational coefficients corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000194
represents an intermediate operation coefficient corresponding to the l-1 st accumulation term, and
Figure BDA0001895173290000195
Figure BDA0001895173290000201
Figure BDA0001895173290000202
further, after obtaining the twiddle factor, the method further includes: storing the twiddle factors (which can be specifically a stored table to obtain a twiddle factor table); the discrete signal data is fast fourier transformed based on the stored twiddle factors, which may be embodied as a twiddle factor table, resulting in a fourier series (embodied as fig. 7, where the first row represents an addition operation, the second row represents a multiplication operation followed by a subtraction operation,
Figure BDA0001895173290000205
representing a twiddle factor).
The data processing method provided by the embodiment of the invention is further explained below.
In view of the above technical problems, embodiments of the present invention provide a data processing method, and in particular, to an optimization method for an FFT algorithm under non-integer frequency shift, which can complete FFT operations without increasing the amount of computation through the modified derivation of FFT butterfly operations; and is applicable to all non-integer frequency shifted carrier frequencies and all butterflies.
The optimization method is mainly characterized in that the expression of FFT butterfly operation is adjusted based on the butterfly operation principle, so that the non-integer frequency shift can be perfectly integrated into the operation process, the split coefficient factors are updated, and the method is not limited to the carrier frequency shift of 1/2, and therefore the FFT operation is completed under the condition that the calculated amount is not increased. The method is not limited to the type of butterfly, and is therefore applicable to all butterflies as well as mixed-radix butterflies.
In the following, the present scheme is exemplified, and the preset discrete signal data is exemplified by discrete time signal data.
1) Radix-2 butterfly:
assuming that the non-integer frequency shift of the carrier is α, the radix-2 butterfly adds the non-integer frequency shift α before it can use S[2][k]To show, for the sake of easy derivation, certain variants are made:
Figure BDA0001895173290000203
wherein ,S[2][k]＝ak(ii) a N represents a minimum positive period of discrete-time signal data; s' [ n ]]Representing discrete time signal data; e represents a natural constant; k represents an integer frequency shift amount of the carrier; s [ n ]]Representing the processed discrete-time signal data,
Figure BDA0001895173290000204
s[2n]is a data sequence s [ n ]]Even terms of (c), corresponding to s [2n +1]]Is s [ n ]]Thereby mixing the data sequence s n]Two cumulative terms are divided. n denotes a time domain, and k denotes a frequency domain. From the point of view of accumulation, n here denotes the nth accumulated term. The value range of N in the first row of the formula (7) is greater than or equal to 0 and less than or equal to N-1; the value range of N in the second row of the formula (7) is greater than or equal to 0 and less than or equal to N/2-1. The value ranges of the two rows k are both more than or equal to 0 and less than or equal to N/2-1.
For convenience of expression, let the 0 th cumulative term representing base 2
Figure BDA0001895173290000211
1 st cumulative term representing radix 2
Figure BDA0001895173290000212
Twiddle factor W ═ e-j2π，
Figure BDA0001895173290000213
Accordingly, equation (7) can be expressed as:
Figure BDA0001895173290000214
wherein ,
Figure BDA0001895173290000215
the superscript denotes base 2 and the subscript denotes the 0 th cumulative term. In the same way
Figure BDA0001895173290000216
The 1 st cumulative term representing radix 2.
In terms of the form of the above-mentioned materials,
Figure BDA0001895173290000217
and S[2][k]The same is true. Thus, it is possible to provide
Figure BDA0001895173290000219
The splitting can continue such that S[2][k]Capable of cyclic splitting, corresponding
Figure BDA00018951732900002110
Can be expressed as:
Figure BDA00018951732900002111
wherein ,
Figure BDA00018951732900002112
n represents a minimum positive period of discrete-time signal data; e represents a natural constant; k represents an integer amount of frequency shift of the carrier. s 2n]Is a data sequence s [ n ]]Even terms of (c), corresponding to s [2n +1]]Is s [ n ]]Thereby mixing the data sequence s n]Two cumulative terms are divided. n denotes a time domain, and k denotes a frequency domain. From the point of view of accumulation, n here denotes the nth accumulated term. The value range of N in the first row of the formula (9) is greater than or equal to 0 and less than or equal to N-1; the value range of N in the second row of the formula (9) is greater than or equal to 0 and less than or equal to N/2-1. The value range of N in the third row of the formula (9) is greater than or equal to 0 and less than or equal to N/2-1. The value ranges of k in the three rows of the formula (9) are all less than or equal to 0 and greater than or equal to N/2-1.
Figure BDA0001895173290000221
Due to the fact that
Figure BDA0001895173290000222
Can also use
Figure BDA0001895173290000223
And
Figure BDA0001895173290000224
perform the representation (thus only N/2 pieces need to be calculated
Figure BDA0001895173290000225
And
Figure BDA0001895173290000226
the value is right; the butterfly uses this to reduce the amount of computation. The formula 9 shows that the scheme can reduce the calculation amount as the traditional butterfly operation, and the reduction amount is the same; so the performance is the same as that of the conventional butterfly operation, and the calculation amount is not increased), so the simplified butterfly operation method supporting the conventional FFT of the present invention has a flowchart as shown in fig. 2.
With respect to equation (9), this is explained herein because
Figure BDA0001895173290000227
Has a period of N/2, so
Figure BDA0001895173290000228
The splitting of equation (7) to the last stage can be expressed as:
Figure BDA0001895173290000229
as can be seen from equation (10), the present solution does not need to perform phase rotation on the carrier of the data sequence, and thus does not need to increase the amount of extra computation.
Now, taking LTE as an example for analysis, in an uplink timeslot of LTE, a time-continuous signal s (t) is shown in formula (3), which is simplified as shown in formula (4), and a corresponding DFT is shown in formula (5). It is easy to find that the carrier frequency in equation (5) includes a frequency shift of 1/2, and in this case, FFT operation cannot be performed directly. In the conventional scheme, as shown in equation (6), carrier phase rotation is performed before FFT operation, and then FFT operation is performed. Therefore, in the conventional scheme, when performing FFT operation, one carrier phase rotation is performed on each data point, i.e., N additional complex multiplication operations are added.
According to the optimization method of the FFT algorithm under the non-integer frequency shift, as shown in formula (7), the carrier frequency non-integer frequency shift α is integrated on the basis of the FFT butterfly operation mathematical expression, so that the discrete time signal s [ N ] does not need to be subjected to carrier phase rotation before FFT operation, and N times of complex multiplication operation is reduced compared with the traditional method.
In LTE, the value of N may be 1024, 2048, and 4096. When the receiving end performs 2048-point FFT operation, equation (7) needs to perform υ ═ log2N11 stages of operation require N times of complex multiplication and complex addition operations per stage, so the total operation times of the complex multiplication and addition is N υ Nlog2N11 × 2048 22528 times. In the conventional method, 2048 times of complex multiplication operations are additionally required, namely N + N upsilon + N log2N12 × 2048 24576, which is added by about 9% of complex multiplication. This solution does not need to increase the number of complex multiplication operations by 9%. In addition, the scheme is also suitable for the condition of non-integer frequency shift of all carrier frequencies, all butterfly operations and mixed-basis butterfly operations.
2) Radix 3 butterfly:
referring to the radix-2 butterfly, the non-integer frequency shift amount of the carrier is set to α, and the radix-3 butterfly under the non-integer frequency shift is represented by the following formula:
Figure BDA0001895173290000231
wherein ,S[3][k]＝ak(ii) a N represents a minimum positive period of discrete-time signal data; s' [ n ]]Representing discrete time signal data; e represents a natural constant; k represents an integer frequency shift amount of the carrier; s [ n ]]Representing the processed discrete-time signal data,
Figure BDA0001895173290000232
s[3n]and s [3n +2]]Is a data sequence s [ n ]]Even terms of (c), corresponding to s [3n +1]]Is s [ n ]]Thereby mixing the data sequence s n]Three accumulation terms are divided. n denotes a time domain, and k denotes a frequency domain. From the point of view of accumulation, n here denotes the nth accumulated term. The value range of N in the first row of the formula (11) is greater than or equal to 0 and less than or equal to N-1; the value range of N in the second row of the formula (11) is greater than or equal to 0 and less than or equal to N/2-1. The value range of N in the third row of the formula (11) is greater than or equal to 0 and less than or equal to N/3-1. The value ranges of the three rows k are all larger than or equal to 0 and smaller than or equal to N/3-1.
Rotation factor
Figure BDA0001895173290000233
Base 3 accumulation term 0
Figure BDA0001895173290000234
Base 3 first accumulation term
Figure BDA0001895173290000235
Base 3, 2 nd accumulation term
Figure BDA0001895173290000236
In terms of the form of the above-mentioned materials,
Figure BDA0001895173290000237
and
Figure BDA0001895173290000238
are all equal to S[3][k]The same is true. Thus, it is possible to provide
Figure BDA0001895173290000239
And
Figure BDA00018951732900002310
can be continuously split, thereby leading S to be[3][k]Capable of cyclic splitting, corresponding
Figure BDA0001895173290000241
And
Figure BDA0001895173290000242
can be respectively expressed as:
Figure BDA0001895173290000243
wherein ,
Figure BDA0001895173290000244
n represents a minimum positive period of discrete-time signal data; e represents a natural constant; k represents an integer amount of frequency shift of the carrier. s 3n]And s [3n +2]]Is a data sequence s [ n ]]Even terms of (c), corresponding to s [3n +1]]Is s [ n ]]Thereby mixing the data sequence s n]Three accumulation terms are divided. n denotes a time domain, and k denotes a frequency domain. From the point of view of accumulation, n here denotes the nth accumulated term. The value range of N in the first row of the formula (12) is greater than or equal to 0 and less than or equal to N-1; the value range of N in the second row of the formula (12) is greater than or equal to 0 and less than or equal to N/2-1. The value range of N in the third row of the formula (12) is greater than or equal to 0 and less than or equal to N/3-1. The value range of N in the fourth row of the formula (12) is greater than or equal to 0 and less than or equal to N/3-1. The value ranges of the four rows k are all larger than or equal to 0 and smaller than or equal to N/3-1.
Rotation factor
Figure BDA0001895173290000245
Base 3 accumulation term 0
Figure BDA0001895173290000246
Base 3 first accumulation term
Figure BDA0001895173290000247
Base 3, 2 nd accumulation term
Figure BDA0001895173290000248
Figure BDA0001895173290000251
wherein ,
Figure BDA0001895173290000252
n represents a minimum positive period of discrete-time signal data; e represents a natural constant; k represents an integer amount of frequency shift of the carrier. s 3n]And s [3n +2]]Is a data sequence s [ n ]]Even terms of (c), corresponding to s [3n +1]]Is s [ n ]]Thereby mixing the data sequence s n]Three accumulation terms are divided. n denotes a time domain, and k denotes a frequency domain. From the point of view of accumulation, n here denotes the nth accumulated term. The value range of N in the first row of the formula (13) is greater than or equal to 0 and less than or equal to N-1; the value range of N in the second row of the formula (13) is greater than or equal to 0 and less than or equal to N/2-1. The value range of N in the third row of the formula (13) is greater than or equal to 0 and less than or equal to N/3-1. The value range of N in the fourth row of the formula (13) is greater than or equal to 0 and less than or equal to N/3-1. The value ranges of the four rows k are all larger than or equal to 0 and smaller than or equal to N/3-1.
Rotation factor
Figure BDA0001895173290000253
Base 3 accumulation term 0
Figure BDA0001895173290000254
Base 3 first accumulation term
Figure BDA0001895173290000255
Base 3, 2 nd accumulation term
Figure BDA0001895173290000256
Therefore, the scheme provided by the embodiment of the present invention is also applicable to the radix-3 butterfly operation, and specifically, refer to the flow chart of the radix-3 butterfly operation shown in fig. 3;
and S can be seen from formula (11) and formula (12)[3][k]Only the first N/3 differences need to be found
Figure BDA0001895173290000257
And
Figure BDA0001895173290000258
the values are such that the butterfly operation is significantly less computationally intensive.
With respect to the formula (12) and the formula (13), the explanation is made here because
Figure BDA0001895173290000261
Is N/3, so
Figure BDA0001895173290000262
3) The general formula of butterfly operation:
from the above, a general formula of butterfly operation can be further obtained, assuming that the non-integer frequency shift amount of the carrier is α, the radix-l butterfly operation under the non-integer frequency shift can use S[l][k]Represents:
Figure BDA0001895173290000263
wherein ,S[l][k]＝ak，akRepresenting a Fourier series, S[l][k]Is shown askPerforming butterfly operation with a radix of l; n represents a minimum positive period of discrete-time signal data; s' [ n ]]Representing discrete time signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; s [ n ]]Representing the processed discrete-time signal data,
Figure BDA0001895173290000264
l represents the radix of butterfly operation as l; s [ ln]Represents the ln-th item of data in the discrete-time signal data; s [ ln +1]]Represents the ln +1 th item of data in the discrete-time signal data; s [ ln +2]]Represents the ln +2 th item of data in the discrete-time signal data; s [ ln + (l-1)]Data representing the ln + (l-1) th item in the discrete-time signal data; s [ ln]And s [ ln +2]]Is a data sequence s [ n ]]Even terms of (1), corresponding to s [ ln +1]Is s [ n ]]S [ ln + (l-1)]Is s [ n ]]Even or odd terms ofItem, whereby a data sequence s [ n ]]Is divided into l accumulation terms.
α denotes the non-integer amount of frequency shift of the carrier;
Figure BDA0001895173290000271
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000272
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000273
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000274
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000275
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA0001895173290000276
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure BDA0001895173290000277
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA0001895173290000278
Figure BDA0001895173290000279
Figure BDA00018951732900002710
Figure BDA00018951732900002711
due to the fact that
Figure BDA00018951732900002712
Has a period of N/l, and from the form,
Figure BDA00018951732900002713
and
Figure BDA00018951732900002714
are all equal to S[l][k]The same is true. Thus, it is possible to provide
Figure BDA00018951732900002715
And
Figure BDA00018951732900002716
can be continuously split, thereby leading S to be[l][k]The circular splitting can be carried out, and the circular splitting can be carried out,
Figure BDA00018951732900002717
all can use
Figure BDA00018951732900002718
To indicate. For example:
Figure BDA0001895173290000281
wherein ,
Figure BDA0001895173290000282
Figure BDA0001895173290000283
the number of fourier series is represented,
Figure BDA0001895173290000284
show that
Figure BDA0001895173290000285
Performing butterfly operation with a radix of l; n represents a minimum positive period of discrete-time signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; l representsThe radix of the butterfly is l; i represents i
Figure BDA0001895173290000286
s[ln]Represents the ln-th item of data in the discrete-time signal data; s [ ln +1]]Represents the ln +1 th item of data in the discrete-time signal data; s [ ln +2]]Represents the ln +2 th item of data in the discrete-time signal data; s [ ln + (l-1)]Data representing the ln + (l-1) th item in the discrete-time signal data; s [ ln]And s [ ln +2]]Is a data sequence s [ n ]]Even terms of (1), corresponding to s [ ln +1]Is s [ n ]]S [ ln + (l-1)]Is s [ n ]]To even or odd terms of the sequence of data s n]Is divided into l accumulation terms.
α denotes the non-integer amount of frequency shift of the carrier;
Figure BDA0001895173290000291
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000292
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000293
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000294
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000295
representing the intermediate operational coefficient corresponding to the 1 st accumulation term,
Figure BDA0001895173290000296
representing the intermediate operational coefficients corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000297
represents an intermediate operation coefficient corresponding to the l-1 st accumulation term, and
Figure BDA0001895173290000298
Figure BDA0001895173290000299
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA00018951732900002910
representing the twiddle factor corresponding to the 2 nd accumulation term,
Figure BDA00018951732900002911
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900002912
Figure BDA00018951732900002913
Figure BDA00018951732900002914
equation (15) represents S[l][k]K in (1) plus arbitrary
Figure BDA00018951732900002915
All can use
Figure BDA00018951732900002916
To indicate.
In summary, the scheme provided by the embodiment of the present invention is not only applicable to radix-2 and radix-3 butterflies, but also applicable to butterflies of all radix, i.e., any butterflies, and the difference between the butterfly and the FFT butterfly lies in the factor
Figure BDA00018951732900002917
Including angle α.
As to the formula (15), the explanation here is made because
Figure BDA00018951732900002918
Is N/l, so
Figure BDA00018951732900002919
4) Mixed-radix butterfly operation
Considering that the mixed-radix butterfly operation includes two or more single-radix butterflies, and the single-radix butterflies can be obtained by equations 14 and 15, the solution provided by the embodiment of the present invention is also applicable to the mixed-radix butterfly operation:
since the single-radix butterfly operation has a certain requirement on the sequence length, r needs to be satisfiedμ. Wherein r is the base number and μ is the corresponding order. It is difficult to satisfy a number of different length sequences. The mixed base is composed of different base numbers, and the limitation on the length of the sequence is reduced to a certain extent. For example, the combination of base 2 and base 3 may be applied to all lengths of
Figure BDA0001895173290000301
The sequence of (a). Because the scheme is suitable for all-radix butterfly operation, the scheme is also suitable for the mixed-radix butterfly operation, and a flow diagram for realizing 6-point DFT by the mixed-radix butterfly operation is shown in FIG. 4; and the scheme is not only applicable to the combination of the base 2 and the base 3, but also applicable to the mixed bases of all other combinations.
Among them, the twiddle factor in FIG. 4
Figure BDA0001895173290000302
Figure BDA0001895173290000303
α denotes the non-integer frequency shift amount of the carrier wave, N denotes the minimum positive period of the discrete-time signal data, and e denotes a natural constant.
From the above, it can be seen that the performance optimization method for the FFT algorithm under the non-integer frequency shift provided in the embodiment of the present invention can complete the FFT operation without increasing the calculation amount, in which:
1) compared with the existing method, the FFT algorithm performance optimization method under non-integer frequency shift provided by the embodiment of the invention can reduce N times of multiplication calculation.
2) The scheme provided by the embodiment of the invention can be applied to all non-integer frequency shifts, and is not only applied to 1/2 frequency shifts in formula (3).
3) The scheme provided by the embodiment of the invention is suitable for all base number and mixed base combinations, and has better compatibility with the traditional FFT operation.
In summary, the scheme provided by the embodiment of the invention can be applied to FFT operations of various bases and mixed bases. Compared with the prior art, the scheme can complete FFT operation without increasing calculated amount, is suitable for all non-integer frequency shifts, is suitable for all base numbers and mixed bases, and has better compatibility with the traditional FFT operation.
An embodiment of the present invention further provides a data processing apparatus, as shown in fig. 5, including: a memory 51, a processor 52 and a computer program 53 stored on the memory 51 and executable on the processor 52; the processor 52, when executing the program, performs the following steps:
carrying out Fourier transform on preset discrete signal data to obtain Fourier series;
splitting the Fourier series to obtain a twiddle factor;
wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave.
The data processing equipment provided by the embodiment of the invention obtains Fourier series by carrying out Fourier transform on preset discrete signal data; splitting the Fourier series to obtain a twiddle factor; wherein, the rotation factor includes non-integer frequency shift amount of carrier wave; the method can realize that the FFT operation is completed under the condition of not increasing the calculation amount, and the data processing amount is reduced, and can be embodied in the following steps: in the uplink time slot of LTE, as the operation times are reduced and the data processing amount is reduced compared with the prior scheme, the processing time delay can be effectively reduced, the processing memory can be saved and the implementation complexity can be reduced; the problem of large processing capacity of a data processing scheme in the prior art is well solved; and the processing mode of the scheme is suitable for all non-integer frequency shifted carrier frequencies and all butterfly operations (including FFT operations of various bases and mixed bases), and has better compatibility with the traditional FFT operation.
Wherein the processor is specifically configured to: splitting the Fourier series by using a formula I to obtain a partial number of twiddle factors;
the first formula is as follows:
Figure BDA0001895173290000311
wherein ,akRepresenting a Fourier series, S[l][k]Is shown askPerforming butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data, e representing a natural constant, N representing an nth accumulation term, N being greater than or equal to 0 and less than or equal to N-1, k representing an integer frequency shift amount of the carrier, k being greater than or equal to 0 and less than or equal to N/l-1, α representing a non-integer frequency shift amount of the carrier, s [ N ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000312
Figure BDA0001895173290000313
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000314
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000315
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000316
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000317
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA0001895173290000318
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure BDA0001895173290000319
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900003110
Figure BDA00018951732900003111
in particular, the method comprises the following steps of,
Figure BDA00018951732900003112
the method specifically comprises the following steps:
Figure BDA0001895173290000321
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000322
Figure BDA0001895173290000323
further, the processor is further configured to: splitting the Fourier series by using a formula II to obtain twiddle factors of the rest number;
the second formula is:
Figure BDA0001895173290000324
wherein ,
Figure BDA0001895173290000325
the number of fourier series is represented,
Figure BDA0001895173290000326
show that
Figure BDA0001895173290000327
Performing butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; i represents i
Figure BDA0001895173290000331
I is more than or equal to 0 and less than or equal to l-1, α represents non-integer frequency shift quantity of carrier wave, s [ n ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000332
Figure BDA0001895173290000333
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000334
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000335
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000336
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000337
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA0001895173290000338
representing the twiddle factor corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000339
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900003310
in particular, the method comprises the following steps of,
Figure BDA00018951732900003311
the method specifically comprises the following steps:
Figure BDA0001895173290000341
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000342
representing the intermediate operational coefficient corresponding to the 1 st accumulation term,
Figure BDA0001895173290000343
representing the intermediate operational coefficients corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000344
represents an intermediate operation coefficient corresponding to the l-1 st accumulation term, and
Figure BDA0001895173290000345
Figure BDA0001895173290000351
Figure BDA0001895173290000352
further, the processor is further configured to: after obtaining the twiddle factor, storing the twiddle factor (which may be specifically a table, obtaining a twiddle factor table); based on the stored twiddle factors (which may be embodied as a twiddle factor table), the discrete signal data is subjected to fast fourier transform to obtain a fourier series (see fig. 7 for an embodied implementation).
The implementation embodiments of the data processing method are all applicable to the embodiment of the data processing device, and the same technical effect can be achieved.
An embodiment of the present invention further provides a data processing apparatus, as shown in fig. 6, including:
the first processing module 61 is configured to perform fourier transform on preset discrete signal data to obtain a fourier series;
a first splitting module 62, configured to split the fourier series to obtain a twiddle factor;
wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave.
The data processing device provided by the embodiment of the invention obtains Fourier series by carrying out Fourier transform on preset discrete signal data; splitting the Fourier series to obtain a twiddle factor; wherein, the rotation factor includes non-integer frequency shift amount of carrier wave; the method can realize that the FFT operation is completed under the condition of not increasing the calculation amount, and the data processing amount is reduced, and can be embodied in the following steps: in the uplink time slot of LTE, as the operation times are reduced and the data processing amount is reduced compared with the prior scheme, the processing time delay can be effectively reduced, the processing memory can be saved and the implementation complexity can be reduced; the problem of large processing capacity of a data processing scheme in the prior art is well solved; and the processing mode of the scheme is suitable for all non-integer frequency shifted carrier frequencies and all butterfly operations (including FFT operations of various bases and mixed bases), and has better compatibility with the traditional FFT operation.
Wherein the first splitting module comprises:
the first splitting submodule is used for splitting the Fourier series by using a formula I to obtain a partial number of twiddle factors;
the first formula is as follows:
Figure BDA0001895173290000361
wherein ,akRepresenting a Fourier series, S[l][k]Is shown askPerforming butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data, e representing a natural constant, N representing an nth accumulation term, N being greater than or equal to 0 and less than or equal to N-1, k representing an integer frequency shift amount of the carrier, k being greater than or equal to 0 and less than or equal to N/l-1, α representing a non-integer frequency shift amount of the carrier, s [ N ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000362
Figure BDA0001895173290000363
represents the 0 th accumulated term of the base l,
Figure BDA0001895173290000364
the 1 st accumulated term representing the base l,
Figure BDA0001895173290000365
the 2 nd accumulated term representing the base l,
Figure BDA0001895173290000366
the l-1 st cumulative term representing the base l;
Figure BDA0001895173290000367
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure BDA0001895173290000368
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure BDA0001895173290000369
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900003610
Figure BDA00018951732900003611
in particular, the method comprises the following steps of,
Figure BDA00018951732900003612
the method specifically comprises the following steps:
Figure BDA00018951732900003613
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000371
Figure BDA0001895173290000372
further, the first splitting module further includes:
the second splitting submodule is used for splitting the Fourier series by using a formula II to obtain the twiddle factors of the rest number;
the second formula is:
Figure BDA0001895173290000373
wherein ,
Figure BDA0001895173290000374
the number of fourier series is represented,
Figure BDA0001895173290000375
show that
Figure BDA0001895173290000376
Performing butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; i represents i
Figure BDA0001895173290000377
I is more than or equal to 0 and less than or equal to l-1, α represents non-integer frequency shift quantity of carrier wave, s [ n ]]Represents the processed preset discrete signal data, and
Figure BDA0001895173290000378
Figure BDA0001895173290000379
represents the 0 th accumulated term of the base l,
Figure BDA00018951732900003710
the 1 st accumulated term representing the base l,
Figure BDA00018951732900003711
the 2 nd accumulated term representing the base l,
Figure BDA00018951732900003712
the l-1 st cumulative term representing the base l;
Figure BDA00018951732900003713
indicating that corresponds to the 1 st accumulated itemThe rotation factor is a function of the rotation factor,
Figure BDA00018951732900003714
representing the twiddle factor corresponding to the 2 nd accumulation term,
Figure BDA00018951732900003715
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure BDA00018951732900003716
in particular, the method comprises the following steps of,
Figure BDA0001895173290000381
the method specifically comprises the following steps:
Figure BDA0001895173290000382
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure BDA0001895173290000383
representing the intermediate operational coefficient corresponding to the 1 st accumulation term,
Figure BDA0001895173290000384
representing the intermediate operational coefficients corresponding to the 2 nd accumulation term,
Figure BDA0001895173290000385
represents an intermediate operation coefficient corresponding to the l-1 st accumulation term, and
Figure BDA0001895173290000391
Figure BDA0001895173290000392
Figure BDA0001895173290000393
further, the data processing apparatus further includes: a first storage module, configured to store the twiddle factor after obtaining the twiddle factor (which may be specifically a storage table, to obtain a twiddle factor table); and a second processing module, configured to perform fast fourier transform on the discrete signal data based on the stored twiddle factor (which may be specifically a twiddle factor table) to obtain a fourier series (see fig. 7 for specific implementation).
The implementation embodiments of the data processing method are all applicable to the embodiment of the data processing device, and the same technical effects can be achieved.
Embodiments of the present invention also provide a computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the data processing method described above.
The implementation embodiments of the data processing method are all applicable to the embodiment of the computer-readable storage medium, and the same technical effects can be achieved.
It should be noted that many of the functional components described in this specification are referred to as modules/sub-modules in order to more particularly emphasize their implementation independence.
In embodiments of the invention, the modules/sub-modules may be implemented in software for execution by various types of processors. An identified module of executable code may, for instance, comprise one or more physical or logical blocks of computer instructions which may, for instance, be constructed as an object, procedure, or function. Nevertheless, the executables of an identified module need not be physically located together, but may comprise disparate instructions stored in different bits which, when joined logically together, comprise the module and achieve the stated purpose for the module.
Indeed, a module of executable code may be a single instruction, or many instructions, and may even be distributed over several different code segments, among different programs, and across several memory devices. Likewise, operational data may be identified within the modules and may be embodied in any suitable form and organized within any suitable type of data structure. The operational data may be collected as a single data set, or may be distributed over different locations including over different storage devices, and may exist, at least partially, merely as electronic signals on a system or network.
When a module can be implemented by software, considering the level of existing hardware technology, a module implemented by software may build a corresponding hardware circuit to implement a corresponding function, without considering cost, and the hardware circuit may include a conventional Very Large Scale Integration (VLSI) circuit or a gate array and an existing semiconductor such as a logic chip, a transistor, or other discrete components. A module may also be implemented in programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices or the like.
While the preferred embodiments of the present invention have been described, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.

Claims (12)

1. A data processing method, comprising:
carrying out Fourier transform on preset discrete signal data to obtain Fourier series;
splitting the Fourier series to obtain a twiddle factor;
wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave.
2. The data processing method of claim 1, wherein the splitting the fourier series to obtain the twiddle factor comprises:
splitting the Fourier series by using a formula I to obtain a partial number of twiddle factors;
the first formula is as follows:
Figure FDA0001895173280000011
wherein ,akRepresenting a Fourier series, S[l][k]Is shown askPerforming butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data, e representing a natural constant, N representing an nth accumulation term, N being greater than or equal to 0 and less than or equal to N-1, k representing an integer frequency shift amount of the carrier, k being greater than or equal to 0 and less than or equal to N/l-1, α representing a non-integer frequency shift amount of the carrier, s [ N ]]Represents the processed preset discrete signal data, and
Figure FDA0001895173280000012
Figure FDA0001895173280000013
represents the 0 th accumulated term of the base l,
Figure FDA0001895173280000014
the 1 st accumulated term representing the base l,
Figure FDA0001895173280000015
the 2 nd accumulated term representing the base l,
Figure FDA0001895173280000016
the l-1 st cumulative term representing the base l;
Figure FDA0001895173280000017
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure FDA0001895173280000018
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure FDA0001895173280000019
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure FDA00018951732800000110
Figure FDA00018951732800000111
3. the data processing method of claim 2,
Figure FDA00018951732800000112
the method specifically comprises the following steps:
Figure FDA0001895173280000021
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure FDA0001895173280000022
Figure FDA0001895173280000023
4. the data processing method according to claim 2 or 3, wherein the splitting the Fourier series to obtain the twiddle factor further comprises:
splitting the Fourier series by using a formula II to obtain twiddle factors of the rest number;
the second formula is:
Figure FDA0001895173280000024
wherein ,
Figure FDA0001895173280000025
the number of fourier series is represented,
Figure FDA0001895173280000026
show that
Figure FDA0001895173280000027
Performing butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; i represents i
Figure FDA0001895173280000031
I is more than or equal to 0 and less than or equal to l-1, α represents non-integer frequency shift quantity of carrier wave, s [ n ]]Represents the processed preset discrete signal data, and
Figure FDA0001895173280000032
Figure FDA0001895173280000033
represents the 0 th accumulated term of the base l,
Figure FDA0001895173280000034
the 1 st accumulated term representing the base l,
Figure FDA0001895173280000035
the 2 nd accumulated term representing the base l,
Figure FDA0001895173280000036
the l-1 st cumulative term representing the base l;
Figure FDA0001895173280000037
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure FDA0001895173280000038
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure FDA0001895173280000039
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure FDA00018951732800000310
5. the data processing method of claim 4,
Figure FDA00018951732800000311
，
the method specifically comprises the following steps:
Figure FDA0001895173280000041
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure FDA0001895173280000042
representing the intermediate operational coefficient corresponding to the 1 st accumulation term,
Figure FDA0001895173280000043
representing the intermediate operational coefficient corresponding to the 2 nd accumulation term,
Figure FDA0001895173280000044
represents an intermediate operation coefficient corresponding to the l-1 st accumulation term, and
Figure FDA0001895173280000045
Figure FDA0001895173280000051
Figure FDA0001895173280000052
6. a data processing apparatus comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor; wherein the processor implements the following steps when executing the program:
carrying out Fourier transform on preset discrete signal data to obtain Fourier series;
splitting the Fourier series to obtain a twiddle factor;
wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave.
7. The data processing device of claim 6, wherein the processor is specifically configured to:
splitting the Fourier series by using a formula I to obtain a partial number of twiddle factors;
the first formula is as follows:
Figure FDA0001895173280000053
wherein ,akRepresenting a Fourier series, S[l][k]Is shown askPerforming butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data, e representing a natural constant, N representing an nth accumulation term, N being greater than or equal to 0 and less than or equal to N-1, k representing an integer frequency shift amount of the carrier, k being greater than or equal to 0 and less than or equal to N/l-1, α representing a non-integer frequency shift amount of the carrier, s [ N ]]Represents the processed preset discrete signal data, and
Figure FDA0001895173280000054
Figure FDA0001895173280000055
represents the 0 th accumulated term of the base l,
Figure FDA0001895173280000056
the 1 st accumulated term representing the base l,
Figure FDA0001895173280000057
the 2 nd accumulated term representing the base l,
Figure FDA0001895173280000058
the l-1 st cumulative term representing the base l;
Figure FDA0001895173280000059
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure FDA00018951732800000510
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure FDA00018951732800000511
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure FDA00018951732800000512
Figure FDA00018951732800000513
8. the data processing device of claim 7,
Figure FDA0001895173280000061
the method specifically comprises the following steps:
Figure FDA0001895173280000062
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure FDA0001895173280000063
Figure FDA0001895173280000064
9. the data processing device of claim 7 or 8, wherein the processor is further configured to:
splitting the Fourier series by using a formula II to obtain twiddle factors of the rest number;
the second formula is:
Figure FDA0001895173280000065
wherein ,
Figure FDA0001895173280000071
the number of fourier series is represented,
Figure FDA0001895173280000072
show that
Figure FDA0001895173280000073
Performing butterfly operation with a radix of l; n represents a minimum positive period of the preset discrete signal data; s' [ n ]]Representing the preset discrete signal data; e represents a natural constant; n represents the nth accumulated term, N is greater than or equal to 0 and less than or equal to N-1; k represents an integer frequency shift amount of the carrier, and k is greater than or equal to 0 and less than or equal to N/l-1; i represents i
Figure FDA0001895173280000074
I is more than or equal to 0 and less than or equal to l-1, α represents non-integer frequency shift quantity of carrier wave, s [ n ]]Represents the processed preset discrete signal data, and
Figure FDA0001895173280000075
Figure FDA0001895173280000076
represents the 0 th accumulated term of the base l,
Figure FDA0001895173280000077
the 1 st accumulated term representing the base l,
Figure FDA0001895173280000078
the 2 nd accumulated term representing the base l,
Figure FDA0001895173280000079
the l-1 st cumulative term representing the base l;
Figure FDA00018951732800000710
representing the twiddle factor corresponding to the 1 st accumulation term,
Figure FDA00018951732800000711
representing the twiddle factor corresponding to the 2 nd accumulated term,
Figure FDA00018951732800000712
represents a twiddle factor corresponding to the l-1 st accumulated term, and
Figure FDA00018951732800000713
10. the data processing device of claim 9,
Figure FDA00018951732800000714
the method specifically comprises the following steps:
Figure FDA0001895173280000081
wherein l represents that the radix of butterfly operation is l; s [ ln ] represents the ln-th item of data in the preset discrete signal data; s [ ln +1] represents the ln +1 th item of data in the preset discrete signal data; s [ ln +2] represents the ln +2 th item of data in the preset discrete signal data; s [ ln + (l-1) ] represents the ln + (l-1) th item of data in the preset discrete signal data;
Figure FDA0001895173280000082
representing the intermediate operational coefficient corresponding to the 1 st accumulation term,
Figure FDA0001895173280000083
representing the intermediate operational coefficient corresponding to the 2 nd accumulation term,
Figure FDA0001895173280000084
represents an intermediate operation coefficient corresponding to the l-1 st accumulation term, and
Figure FDA0001895173280000085
Figure FDA0001895173280000091
Figure FDA0001895173280000092
11. a data processing apparatus, comprising:
the first processing module is used for carrying out Fourier transform on preset discrete signal data to obtain Fourier series;
the first splitting module is used for splitting the Fourier series to obtain a twiddle factor;
wherein, the rotation factor includes non-integer frequency shift amount of the carrier wave.
12. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the data processing method according to any one of claims 1 to 5.
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